SOLUTION: Solve each system by the substitution method. x+3y=2 and -x+y=1

Question 175915: Solve each system by the substitution method.
x+3y=2 and -x+y=1
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations (note: I've rearranged the equations):

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Add to both sides

Rearrange the equation

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Subtract 3 from both sides

Combine like terms on the right side

Divide both sides by 4 to isolate x

Reduce

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

which form the ordered pair

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